2026年GRE考試數(shù)學(xué)部分測試及答案考試時(shí)長：120分鐘滿分：100分班級(jí)：__________姓名：__________學(xué)號(hào)：__________得分：__________試卷名稱：2026年GRE考試數(shù)學(xué)部分測試及答案考核對(duì)象：準(zhǔn)備參加2026年GRE考試的考生題型分值分布：-判斷題（總共10題，每題2分）總分20分-單選題（總共10題，每題2分）總分20分-多選題（總共10題，每題2分）總分20分-案例分析（總共3題，每題6分）總分18分-論述題（總共2題，每題11分）總分22分總分：100分---一、判斷題（每題2分，共20分）1.Thesetofintegersisclosedunderdivision.2.Ifafunctioniscontinuousonaclosedinterval,itmustattainitsmaximumandminimumvaluesonthatinterval.3.Theequation\(x^2+y^2=1\)representsacirclecenteredattheoriginwithradius1.4.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).5.Thesumoftheinterioranglesofatriangleisalways180degrees.6.Amatrixwithallelementsequalto1isinvertible.7.Theprobabilityofrollingasumof7withtwofairsix-sideddiceis\(\frac{1}{6}\).8.Themedianofadatasetisalwaysequaltoitsmean.9.Theareaofasquareisgivenbytheformula\(A=s^2\),where\(s\)isthelengthofaside.10.ThePythagoreantheoremappliestoalltriangles.二、單選題（每題2分，共20分）1.Whatisthevalueof\(\frac{3}{4}+\frac{2}{3}\)?A.\(\frac{17}{12}\)B.\(\frac{5}{7}\)C.\(\frac{11}{12}\)D.\(\frac{7}{12}\)2.If\(f(x)=2x-5\),whatis\(f(3)\)?A.1B.4C.6D.73.Theslopeofthelinepassingthroughthepoints\((1,2)\)and\((3,8)\)is:A.3B.2C.1D.\(\frac{1}{3}\)4.Whatisthesimplifiedformof\(\frac{x^2-4}{x-2}\)?A.\(x+2\)B.\(x-2\)C.\(x^2+2\)D.\(x-4\)5.Thevalueof\(\sqrt{50}\)roundedtothenearestintegeris:A.7B.8C.9D.106.Ifabagcontains5redballsand3blueballs,whatistheprobabilityofdrawingaredball?A.\(\frac{1}{2}\)B.\(\frac{3}{8}\)C.\(\frac{5}{8}\)D.\(\frac{2}{3}\)7.Theequation\(2x+3y=6\)canberewritteninslope-interceptformas:A.\(y=\frac{2}{3}x+2\)B.\(y=-\frac{2}{3}x+2\)C.\(y=3x+2\)D.\(y=-3x+2\)8.Thevolumeofacubewithedgelength4is:A.16B.24C.32D.649.If\(f(x)=x^2\)and\(g(x)=x+1\),whatis\((f\circg)(2)\)?A.5B.6C.8D.910.Thenumber0.25inscientificnotationis:A.\(2.5\times10^{-1}\)B.\(2.5\times10^1\)C.\(1.25\times10^{-1}\)D.\(1.25\times10^1\)三、多選題（每題2分，共20分）1.Whichofthefollowingareprimenumbers?A.2B.3C.4D.52.Thegraphofthefunction\(y=x^2\)is:A.AstraightlineB.AparabolaopeningupwardsC.AparabolaopeningdownwardsD.Ahyperbola3.Thepropertiesofaparallelograminclude:A.OppositesidesareparallelB.OppositesidesareequalinlengthC.OppositeanglesareequalD.Adjacentanglesaresupplementary4.Thesolutionstotheequation\(x^2-5x+6=0\)are:A.2B.3C.-2D.-35.Thefollowingarefunctions:A.\(y=3x+2\)B.\(y=\frac{1}{x}\)C.\(y=x^2-4\)D.\(y=2x+3x\)6.Themeasuresoftheinterioranglesofaquadrilateralare:A.90degreesB.100degreesC.110degreesD.120degrees7.Thefollowingarepropertiesofexponents:A.\(a^m\cdota^n=a^{m+n}\)B.\((a^m)^n=a^{mn}\)C.\(\frac{a^m}{a^n}=a^{m-n}\)D.\(\sqrt{a}=a^{\frac{1}{2}}\)8.Thefollowingaretypesoftrianglesbasedonangles:A.AcutetriangleB.RighttriangleC.ObtusetriangleD.Equilateraltriangle9.Thefollowingarepropertiesoflogarithms:A.\(\log_b(xy)=\log_b(x)+\log_b(y)\)B.\(\log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y)\)C.\(\log_b(x^n)=n\log_b(x)\)D.\(\log_b(b)=1\)10.Thefollowingaregeometricsequences:A.2,4,8,16,...B.3,6,9,12,...C.5,10,20,40,...D.1,3,5,7,...四、案例分析（每題6分，共18分）1.Acompanyproduceswidgetsatacostof\$2perwidget.Thesellingpriceperwidgetis\$5.Thecompanyalsoincursafixedmonthlycostof\$1,000.a.Writeanequationforthetotalcost\(C\)intermsofthenumberofwidgetsproduced\(x\).b.Writeanequationforthetotalrevenue\(R\)intermsofthenumberofwidgetssold\(x\).c.Whatisthebreak-evenpoint(i.e.,thenumberofwidgetsthatmustbesoldtocovercosts)?2.Adatasetconsistsofthefollowingnumbers:4,7,9,12,15,18,20.a.Calculatethemeanofthedataset.b.Calculatethemedianofthedataset.c.Calculatethemodeofthedataset.3.Arectanglehasalengthof10cmandawidthof6cm.a.Calculatetheperimeteroftherectangle.b.Calculatetheareaoftherectangle.c.Iftherectangleisscaledbyafactorof2,whatarethenewdimensions,perimeter,andarea?五、論述題（每題11分，共22分）1.Explaintheconceptofafunctioninmathematics.Provideanexampleofafunctionanddescribeitsdomainandrange.Discusstheimportanceoffunctionsinreal-worldapplications.2.Describethepropertiesofacircle.Explainhowtheequationofacircleisderivedfromitsgeometricdefinition.Provideanexampleofareal-worldscenariowherethepropertiesofacirclearerelevant.---標(biāo)準(zhǔn)答案及解析一、判斷題1.False.Thesetofintegersisnotclosedunderdivisionbecausedividingtwointegersmaynotresultinaninteger(e.g.,\(3\div2=1.5\)).2.True.BytheExtremeValueTheorem,acontinuousfunctiononaclosedintervalattainsitsmaximumandminimumvalues.3.True.Theequation\(x^2+y^2=1\)representsacirclecenteredattheoriginwithradius1.4.True.Thederivativeof\(f(x)=x^3\)is\(f'(x)=3x^2\).5.True.Thesumoftheinterioranglesofatriangleisalways180degrees.6.False.Amatrixwithallelementsequalto1isnotinvertibleunlessitistheidentitymatrix.7.False.Theprobabilityofrollingasumof7withtwofairsix-sideddiceis\(\frac{6}{36}=\frac{1}{6}\).8.False.Themedianisthemiddlevaluewhenthedataissorted,whilethemeanistheaverage.9.True.Theareaofasquareisgivenbytheformula\(A=s^2\),where\(s\)isthelengthofaside.10.False.ThePythagoreantheoremappliesonlytorighttriangles.二、單選題1.A.\(\frac{3}{4}+\frac{2}{3}=\frac{9}{12}+\frac{8}{12}=\frac{17}{12}\)2.D.\(f(3)=2(3)-5=6-5=7\)3.A.Theslope\(m=\frac{8-2}{3-1}=\frac{6}{2}=3\)4.A.\(\frac{x^2-4}{x-2}=\frac{(x-2)(x+2)}{x-2}=x+2\)(for\(x\neq2\))5.B.\(\sqrt{50}\approx7.07\),roundedtothenearestintegeris8.6.C.Theprobabilityis\(\frac{5}{5+3}=\frac{5}{8}\).7.A.\(2x+3y=6\implies3y=-2x+6\impliesy=-\frac{2}{3}x+2\).8.D.Thevolumeofacubeis\(4^3=64\).9.A.\((f\circg)(2)=f(g(2))=f(2+1)=f(3)=3^2=9\).10.A.\(0.25=2.5\times10^{-1}\).三、多選題1.A,B,D.2,3,and5areprimenumbers.2.B.Thegraphof\(y=x^2\)isaparabolaopeningupwards.3.A,B,C,D.Oppositesidesareparallel,equalinlength,andadjacentanglesaresupplementary.4.A,B.Thesolutionsare\(x=2\)and\(x=3\).5.A,B,C.Allarefunctions.6.A,B,C,D.Thesumofinterioranglesofaquadrilateralis360degrees,soanycombinationofanglescanbe90,100,110,or120degrees.7.A,B,C,D.Allarepropertiesofexponents.8.A,B,C.Typesoftrianglesbasedonanglesincludeacute,right,andobtusetriangles.9.A,B,C,D.Allarepropertiesoflogarithms.10.A,C.2,4,8,16and5,10,20,40aregeometricsequences.四、案例分析1.a.\(C(x)=2x+1000\)b.\(R(x)=5x\)c.Break-evenpoint:\(C(x)=R(x)\implies2x+1000=5x\implies3x=1000\impliesx=\frac{1000}{3}\approx333.33\).Thecompanymustsell334widgetstobreakeven.2.a.Mean:\(\frac{4+7+9+12+15+18+20}{7}=\frac{85}{7}\approx12.14\).b.Median:Thesorteddatais4,7,9,12,15,18,20.Themedianis12.c.Mode:Thereisnomode(allvaluesappearonce).3.a.Perimeter:\(2(10+6)=32\)cm.b.Area:\(10\times6=60\)cm2.c.Scaleddimensions:\(2\times10=20\)cm,\(2\times6=12\)cm.